Particles don't collide with rigid bodies
I see what you were trying to do with the Soft Body Physics, but what you really need is a Rigid Body Physics simulation. You can learn a bit about it in this quick, fun tutorial, but it is basically a simplified physics engine for gravity and whatever else you want to have affect your meshes.

For the falling-through-the-bottom-box issue, I turned off Collision Physics for all of the meshes except the floor because it has to deal with the particles. I changed some settings to make the particles bounce nicer. I also added all of the meshes to the Rigid Body Physics simulation. You can tell this because when you select them, the outline is green instead of orange. Additionally, I adjusted the particle settings so that they began emitting at the collision of the two boxes.

Final result:



Here is the modified .blend file: